A New Fuzzy Logic-Based Similarity Measure Applied to LargeGap Imputation for Uncorrelated Multivariate Time Series

The completion of missing values is a prevalent problem in many domains of pattern recognition and signal processing. Analyzing data with incompleteness may lead to a loss of power and unreliable results, especially for large missing subsequence(s). Therefore,this paper aims to introduce a new approach for filling successive missing values in low/uncorrelated multivariate time series which allows managing a high level of uncertainty. In this way, we propose using a novel fuzzy weighting-based similarity measure. The proposed method involves three main steps. Firstly, for each incomplete signal, the data before a gap and the data after this gap areconsidered as two separated reference time series with their respective query windows𝑄𝑏and𝑄𝑎. We then find the most similarsubsequence (𝑄𝑏𝑠) to the subsequence before this gap𝑄𝑏and the most similar one (𝑄𝑎𝑠) to the subsequence after the gap𝑄𝑎.Tofind these similar windows, we build a new similarity measure based on fuzzy grades of basic similarity measures and on fuzzy logic rules. Finally, we fill in the gap with average values of the window following𝑄𝑏𝑠and the one preceding𝑄𝑎𝑠. The experimental results have demonstrated that the proposed approach outperforms the state-of-the-art methods in case of multivariate time serieshaving low/noncorrelated data but effective information on each signal.